Abstract
Springer fibers are subvarieties of the flag variety parameterized by nilpotent matrices. They are central objects of study in geometry representation theory. This dissertation focuses on two-row Springer fibers, those corresponding to nilpotent matrices with two Jordan blocks. Irreducible components of two-row Springer fibers are in bijection with two-row standard Young tableaux and also with noncrossing matchings. Inspired by the combinatorial commutative algebra of matrix Schubert varieties, we define a polynomial ideal for each noncrossing matching and prove that these ideals define the corresponding components of the Springer fiber. Our proofs leverage geometric descriptions of Springer fibers established by Fung, Stroppel–Webster, Fresse, and Goldwasser–Nadeem– Sun–Tymoczko. Using these ideals to compute examples, we give two conjectural formulas for the cohomology class of each component of a two-row Springer fiber. We apply commutative algebra techniques to prove these conjectures for a specific family of two-row tableaux.
Committee Chair
Martha Precup
Committee Members
Carl Lian; Hsin-Chieh Liao; John Shareshian; Laura Escobar
Degree
Doctor of Philosophy (PhD)
Author's Department
Mathematics
Document Type
Dissertation
Date of Award
6-19-2026
Language
English (en)
DOI
https://doi.org/10.7936/w8ta-kd80
Recommended Citation
Sabando Alvarez, Maria Cristina, "Ideals Defining Components of Two-row Springer Fibers" (2026). Arts & Sciences Graduate Student Theses and Dissertations. 3829.
The definitive version is available at https://doi.org/10.7936/w8ta-kd80